We are interested in studying the following sum, which is the von Mangoldt convolution analogue to the problem in Section 5 of
[1]}:
\(\mathcal {S}^U_{\Lambda _k,n,Q}(A)=\sum _{\begin{array}{c}f\in \mathcal {M}_n\\f\equiv A\,(\mathrm {mod}\,Q)\end{array}}\Lambda _k(f),\) 
